Berezinskii–Kosterlitz–Thouless transition – A universal neural network study with benchmarks

An autoencoder (AE) and a generative adversarial network (GAN) are trained only once on a one-dimensional (1D) lattice of 200 sites. Moreover, the AE contains only one hidden layer consisting of two neurons and both the generator and the discriminator of the GANs are made up of two neurons as well. The training set employed to train both the considered unsupervised neural networks (NN) is composed of two artificial configurations. Remarkably, despite their simple architectures, both the built AE and GAN have precisely determined the critical points of several models, including the three-dimensional (3D) classical O(3) model, the two-dimensional (2D) generalized classical XY model, the 2D two-state Potts model, and the 1D Bose-Hubbard model. In addition, a factor of few thousands in the speed of calculation is gained for the bulit AE and GAN when they are compared with the conventional unsupervised NN approaches. The results presented here as well as that shown previously in the literature suggest that when phase transitions are considered, an elegant universal neural network that is extremely efficient and is applicable to broad physical systems can be constructed with ease. In particular, since a NN trained with two configurations can be applied to many models, it is likely that when machine learning is concerned, the majority of phase transitions belong to a class having two elements, i.e. the Ising class.

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A universal training scheme and the resulting universality for machine learning phases

Yseng

Jiang

Huang

2022

Progress of Theoretical and Experimental Physics

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Berezinskii–Kosterlitz–Thouless Transition of the Two-Dimensional XY Model on the Honeycomb Lattice

Jiang

2024

Progress of Theoretical and Experimental Physics

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The Berezinskii–Kosterlitz–Thouless (BKT) transition of the two-dimensional XY model on the honeycomb lattice is investigated using both the techniques of Neural network (NN) and Monte Carlo simulations. It is demonstrated in the literature that with certain plausible assumptions, the associated critical temperature TBKT, H is found to be $\frac{1}{\sqrt{2}}$ exactly. Surprisingly, the value of TBKT, H obtained from our NN calculations is 0.572(3) which deviates significantly from $\frac{1}{\sqrt{2}}$. In addition, based on the helicity modulus, the TBKT, H determined is 0.576(4) agreeing well with that resulting from the NN estimation. It will be interesting to carry out a more detailed analytic calculation to obtain a theoretical value consistent with the numerical result reached here.

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Clustering neural quantum states via diffusion maps

Teng,

Sachdev,

Scheurer

2023

Phys. Rev. B

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Berezinskii–Kosterlitz–Thouless transition – A universal neural network study with benchmarks

Cited by 4 publications

References 29 publications

A universal training scheme and the resulting universality for machine learning phases

A universal training scheme and the resulting universality for machine learning phases

Berezinskii–Kosterlitz–Thouless Transition of the Two-Dimensional XY Model on the Honeycomb Lattice

Clustering neural quantum states via diffusion maps

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